New ray packet paper

Solomon Boulos and friends have shown that ray packets may work for secondary rays. Check out the first paper here. As much as I hate the software engineering implications that arise with ray packets, I do like that they can make things faster.

Ray tracing bilinear patches

I'm going to try to reimplement the displacement map method I did with Brian Smits and Mike Stark a few years ago. A key part of that method is intersecting bilinear patches. Given a ray o+tv and a patch with vertices p00, p01, p11, and p10 we have

o + tv = (1-u)(1-v)p00 + u(1-v)p10 + (1-u)v p01 + uv p11

This is three equations (x, y, and z) and three unknowns (t, u, v). The way Brian and I solved this was to eliminate t by using 2 of the equations and then solve the uv system directly. A similar approach is used in Shaun Ramsey et al.'s jgt paper. This has always been unsatisfactory to me because it chooses an arbitrary ordering of the dimensions. Perhaps a numeric solution would be more robust?

Another possibility is to use Kajiya's old trick. Consider the ray as the intersection of two planes

(p - p0) dot N0 = 0
(p - p1) dot N1 = 0

If you substitute
p = (1-u)(1-v)p00 + u(1-v)p10 + (1-u)v p01 + uv p11

into both the plane equations above then you get two equations in uv of the form:
Auv + Bu + Cv + D = 0 (1)
auv + bu + cv + d = 0 (2)

If you solve one of those for u and then plug it into the other, you get a quadratic in v. That leaves four possibilities of what to do first:

solve (1) for u
solve (1) for v
solve (2) for u
solve (2) for v

There is also a degree of freedom for which planes to use. In any case seems more stable than the three equations, 2 unknowns method above.

How long before interactive ray tracing is on the desktop?

Solomon Boulos and friends in our group at Utah have their ray tracer going about 1 frame per second on one core of a 2GHz Opteron 870 with one ray per pixel at a million pixels. This is with full shadows and reflections so is slower than a lot of the numbers you see in the literature. For NTSC resolution (640x480) that would be more like 3-4 frames per second. So we'd need about 8 of those cores for fluid motion. So we are right on the threshold for such low resolutions. If Intel comes through with its 60 core chip, and ray tracing maps to it, then HDTV resolution and some multisampling should be straightforward. The Cell is also a possibility as shown by Carsten Benthin and his collaborators in their recent papers. We could get ray tracing even sooner if an ASIC is built. I don't see why a game box based on ray tracing would not be feasible now.